Ellipse perimeter calculator

Perimeter is the distance around a two-dimensional shape.

Ellipse — is a closed curve on a plane that can be obtained as the intersection of a plane and a circular cylinder or as an orthogonal projection of a circle onto a plane.

An ellipse is a curve that is defined by its two axes, a major axis and a minor axis. The perimeter of an ellipse is the distance around the outside of the curve. To find the perimeter of an ellipse, we need to find the length of two semi-axes or the length of two axes of an ellipse (maximum and minimum length of an ellipse). After we know the indicated values, we can apply the following formula for calculating the perimeter of an ellipse:

P = 2 \pi \sqrt{\dfrac{R^2 + r^2}{2}}

where:

• P is the perimeter of the ellipse
• R is the length of the semi-major axis
• r is the length of the semi-minor axis

How to Use the Ellipse Perimeter Calculator

Our ellipse perimeter calculator makes it easy to find the perimeter of your ellipse. To use the calculator:

1. Enter the length of the semi-minor axis (r) in the first box.
2. Enter the length of the semi-major axis (R) in the second box.
3. The calculator will automatically display the perimeter of the ellipse.

Ellipse Perimeter Formula Examples

Here are some examples of finding the perimeter of an ellipse using the formula:

Example 1

Find the perimeter of an ellipse with a semi-major axis of 5 and a semi-minor axis of 3.

P = 2 \pi \sqrt{\dfrac{5^2 + 3^2}{2}}

P = 2 \pi \sqrt{\dfrac{34}{2}}

P = 2 \pi \sqrt{17}

P ≈ 20.4

Example 2

Find the perimeter of an ellipse with a semi-major axis of 8 and a semi-minor axis of 6.

P = 2 \pi \sqrt{\dfrac{8^2 + 6^2}{2}}

P = 2 \pi \sqrt{100}

P ≈ 35.4

Conclusion

Calculating the perimeter of an ellipse is an important skill in geometry. Our ellipse perimeter calculator and formula make it easy to find the perimeter of your ellipse. Try it out for yourself and see how easy it can be!